{
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    "accelerator": "GPU",
    "colab": {
      "name": "American_Option_Black_Scholes.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "EheA5_j_cEwc"
      },
      "source": [
        "##### Copyright 2019 Google LLC.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "YCriMWd-pRTP",
        "colab": {}
      },
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "OvRwFTkqcp1e"
      },
      "source": [
        "# American Option Pricing in TFF under the Black-Scholes Model\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/google/tf-quant-finance/blob/master/tf_quant_finance/examples/jupyter_notebooks/American_Option_Black_Scholes.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/google/tf-quant-finance/blob/master/tf_quant_finance/examples/jupyter_notebooks/American_Option_Black_Scholes.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "uG8UAZXjeUhf",
        "colab": {}
      },
      "source": [
        "#@title Upgrade to TensorFlow 2.1+\n",
        "!pip install --upgrade tensorflow"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "aijwbAA8u_IM",
        "colab": {}
      },
      "source": [
        "#@title Install TF Quant Finance\n",
        "!pip install tf-quant-finance"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "roUegEh5eh04",
        "colab": {}
      },
      "source": [
        "#@title Install QuantLib\n",
        "!pip install QuantLib-Python"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ku46LPe6Jswv"
      },
      "source": [
        "### This notebook demonstrates the use of low level Tensorflow Quant Finance tools for American Option pricing under the Black-Scholes model with emphasis on the following aspects:\n",
        "\n",
        "  * **Batching**: Tensorflow is vectorized out of the box. Tensorflow Finance (TFF) written to leverage this wherever possible.\n",
        "    * Most methods accept a \"batch\" of inputs.\n",
        "  * **Hardware Accelerators**: Tensorflow supports GPUs without any significant code changes. Significant speedups with no code change.\n",
        "    * Write the model once and run it on CPU or GPU.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "2nA2FSdTgcEM",
        "colab": {}
      },
      "source": [
        "#@title Imports { display-mode: \"form\" }\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import time\n",
        "\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "\n",
        "import tensorflow as tf\n",
        "\n",
        "# tff for Tensorflow Finance\n",
        "import tf_quant_finance as tff \n",
        "\n",
        "# Shortcut alias\n",
        "pde = tff.math.pde\n",
        "\n",
        "from IPython.core.pylabtools import figsize\n",
        "figsize(21, 14)  # better graph size for Colab  \n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\",\n",
        "                        category=FutureWarning)  # suppress printing warnings\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "KsVBo68Fabgt"
      },
      "source": [
        " ### Setup American Option pricer\n",
        "   American option price $V(x, t)$ of an option with spot price $x$ at time $t$\n",
        "   under Black-Scholes model satisfies the following PDE\n",
        "   $$V_{t} + \\frac{\\sigma^2}{2}  x^2  V_{xx} + r  x  V_{x}\n",
        " - r  V(t, x) = 0.$$\n",
        "  Tensorflow Quant Finance library provides tools for solving Parabolic PDE's\n",
        "  of the form  \n",
        "  $$V_{t} + \\frac{a(t, x)}{2}  V_{xx} + b(t, x) V_{x} - c(t, x)  V = 0$$\n",
        "\n",
        "  Henceforth,\n",
        "  $a(t, x)$, $b(t, x)$, and $c(t, x)$ are referred to as quadratic, linear and\n",
        "  shift coefficients, respectively. We describe in details how to write a\n",
        "  custom pricer that is both batchable (i.e., multiple equations can be solved\n",
        "  simultaneously) and compatible with an NVIDIA GPU. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "13_gS0ZIBw2x",
        "colab": {}
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      "source": [
        "#@title American Option pricer\n",
        "\n",
        "# tf.function decorator makes the function faster in graph mode.\n",
        "# Autograph is disabled in order to depracate the warnings\n",
        "@tf.function(autograph=False)\n",
        "def american_option(number_grid_points,\n",
        "                    time_delta,\n",
        "                    strike,\n",
        "                    volatility,\n",
        "                    risk_free_rate,\n",
        "                    expiry,\n",
        "                    dtype=tf.float64):\n",
        "  \"\"\" Computes American Call options prices.\n",
        "\n",
        "  Args:\n",
        "    number_grid_points: A Python int. Number of grid points for the finite\n",
        "      difference scheme.\n",
        "    time_delta: A Python float. Grid time discretization parameter.\n",
        "    strike: A real `Tensor` of shape `(number_of_options, 1)`.\n",
        "      Represents the strikes of the underlying American options. \n",
        "    volatility: A real `Tensor` of shape `(number_of_options, 1)`.\n",
        "      Represents the volatilities of the underlying American options. \n",
        "    risk_free_rate: A real `Tensor` of shape `(number_of_options, 1)`.\n",
        "      Represents the risk-free interest rates associated with the underlying\n",
        "      American options.\n",
        "    expiry: A Python float. Expiry date of the options. If the options\n",
        "      have different expiries, volatility term has to adjusted to\n",
        "      make expiries the same.\n",
        "    dtype: Optional `tf.dtype` used to assert dtype of the input `Tensor`s.\n",
        "\n",
        "  Returns:\n",
        "    A tuple of the estimated option prices of shape\n",
        "    `(number_of_options, number_grid_points)` and the corresponding `Tensor` \n",
        "    of grid locations of shape `(number_grid_points,)`.\n",
        "  \"\"\"\n",
        "  # Define the coordinate grid\n",
        "  s_min = 0.01\n",
        "  s_max = 300.\n",
        "  grid = pde.grids.uniform_grid(minimums=[s_min],\n",
        "                                maximums=[s_max],\n",
        "                                sizes=[number_grid_points],\n",
        "                                dtype=dtype)\n",
        "\n",
        "  # Define the values grid for the final condition\n",
        "  s = grid[0]\n",
        "  final_values_grid = tf.nn.relu(s - strike)\n",
        "\n",
        "  # Define the PDE coefficient functions\n",
        "  def second_order_coeff_fn(t, grid):\n",
        "    del t\n",
        "    s = grid[0]\n",
        "    return [[volatility ** 2 * s ** 2 / 2]]\n",
        "\n",
        "  def first_order_coeff_fn(t, grid):\n",
        "    del t\n",
        "    s = grid[0]\n",
        "    return [risk_free_rate * s]\n",
        "\n",
        "  def zeroth_order_coeff_fn(t, grid):\n",
        "    del t, grid\n",
        "    return -risk_free_rate\n",
        "\n",
        "  # Define the boundary conditions\n",
        "  @pde.boundary_conditions.dirichlet\n",
        "  def lower_boundary_fn(t, grid):\n",
        "    del t, grid\n",
        "    return tf.constant(0.0, dtype=dtype)\n",
        "\n",
        "  @pde.boundary_conditions.dirichlet\n",
        "  def upper_boundary_fn(t, grid):\n",
        "    del grid\n",
        "    return tf.squeeze(s_max - strike * tf.exp(-risk_free_rate * (expiry - t)))\n",
        "\n",
        "  # In order to price American option one needs to set option values to \n",
        "  # V(x) := max(V(x), max(x - strike, 0)) after each iteration\n",
        "  def values_transform_fn(t, grid, values):\n",
        "    del t\n",
        "    s = grid[0]\n",
        "    values_floor = tf.nn.relu(s - strike)\n",
        "    return grid, tf.maximum(values, values_floor)\n",
        "\n",
        "  # Solve\n",
        "  estimate_values, estimate_grid, _, _ = \\\n",
        "    pde.fd_solvers.solve_backward(\n",
        "      start_time=expiry,\n",
        "      end_time=0,\n",
        "      values_transform_fn=values_transform_fn,\n",
        "      coord_grid=grid,\n",
        "      values_grid=final_values_grid,\n",
        "      time_step=time_delta,\n",
        "      boundary_conditions=[(lower_boundary_fn, upper_boundary_fn)],\n",
        "      second_order_coeff_fn=second_order_coeff_fn,\n",
        "      first_order_coeff_fn=first_order_coeff_fn,\n",
        "      zeroth_order_coeff_fn=zeroth_order_coeff_fn,\n",
        "      dtype=dtype\n",
        "    )\n",
        "  return estimate_values, estimate_grid[0]\n",
        "\n",
        "\n",
        "def option_param(number_of_options, dtype, seed=42):\n",
        "  \"\"\" Function to generate volatilities, rates, strikes \"\"\"\n",
        "  np.random.seed(seed)\n",
        "  if number_of_options > 1:\n",
        "    volatility = tf.random.uniform(shape=(number_of_options, 1),\n",
        "                                   dtype=dtype) * 0.1 + 0.3\n",
        "    # Random risk free rate between 0 and 0.2.\n",
        "    risk_free_rate = tf.constant(\n",
        "      np.random.rand(number_of_options, 1) * 0.05, dtype)\n",
        "    # Random strike between 20 and 120.\n",
        "    strike = tf.constant(\n",
        "      np.random.rand(number_of_options, 1) * 100 + 50, dtype)\n",
        "  else:\n",
        "    volatility = tf.constant([0.3], dtype)\n",
        "    risk_free_rate = tf.constant([0.05], dtype)\n",
        "    strike = tf.constant([50], dtype)\n",
        "  return volatility, risk_free_rate, strike"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "OnijmIHSD5_a"
      },
      "source": [
        "### Batching\n",
        "\n",
        "* Batching is a powerful feature of design of Tensorflow.\n",
        "* TFF leverages this strongly.\n",
        "* Most methods can accept a \"batch\" of inputs.\n",
        "* Example below (Batch of American Call Options with varying strikes, vols and rates).\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "qAPYRpLIEgPH",
        "colab": {}
      },
      "source": [
        "#@title Price multiple American Call options at a time\n",
        "\n",
        "number_of_options = 10 #@param\n",
        "\n",
        "time_delta = 0.005\n",
        "\n",
        "expiry = 1.0  \n",
        "\n",
        "number_grid_points = 1024 \n",
        "\n",
        "dtype = tf.float64 \n",
        "\n",
        "spot = 110  + tf.random.uniform(shape=[number_of_options, 1], dtype=dtype)\n",
        "\n",
        "# Generate volatilities, rates, strikes\n",
        "volatility, risk_free_rate, strike = option_param(number_of_options, dtype)\n",
        "\n",
        "# Build a graph to compute prices of the American Options.\n",
        "estimate, grid_locations = american_option(\n",
        "    time_delta=time_delta,\n",
        "    expiry=expiry,\n",
        "    number_grid_points=number_grid_points,\n",
        "    volatility=volatility,\n",
        "    risk_free_rate=risk_free_rate,\n",
        "    strike=strike,\n",
        "    dtype=dtype)\n",
        "\n",
        "# Convert to numpy for plotting\n",
        "estimate = estimate.numpy()\n",
        "grid_locations = grid_locations.numpy()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "I7eAh-_Z3jdK",
        "outputId": "c434408e-8344-45fe-fdbd-2885ce207bc9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 535
        }
      },
      "source": [
        "#@title Price/spot plot for the American Call options\n",
        "# Prepare data for plotting \n",
        "options = [x + 1 for x in range(number_of_options) for _ in range(1024)]\n",
        "plot_data = pd.DataFrame({\n",
        "    'Spot': list(np.ndarray.flatten(grid_locations)) * number_of_options, \n",
        "    'Price': estimate.flatten(),\n",
        "    'Option': options})\n",
        "\n",
        "\n",
        "# Plot\n",
        "plt.figure(figsize=(10, 8))\n",
        "sns.set(style=\"darkgrid\")\n",
        "sns.set_context(\"paper\", font_scale=1.5, rc={\"lines.linewidth\": 2.5})\n",
        "plot = sns.lineplot(x=\"Spot\", y=\"Price\", hue=\"Option\",\n",
        "                    data=plot_data,\n",
        "                    palette=sns.color_palette()[:number_of_options],\n",
        "                    legend=False)\n",
        "plot.axes.set_title(f\"Price/Spot for {number_of_options} American Call Options\",\n",
        "                    fontsize=25)\n",
        "xlabel = plot.axes.get_xlabel()\n",
        "ylabel = plot.axes.get_ylabel()\n",
        "plot.axes.set_xlabel(xlabel, fontsize=20)\n",
        "plot.axes.set_ylabel(ylabel, fontsize=20)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "B4Y5lQV3S9l8"
      },
      "source": [
        "### Speedup from batching\n",
        "\n",
        "* Price of 5000 American Call options. Time comparison with QuantLib"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "YCWMBrv-S87k",
        "outputId": "5fd454af-9d71-4386-c63d-4812874d1319",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        }
      },
      "source": [
        "#@title Tensorflow Finance pricing on GPU\n",
        "\n",
        "number_of_options = 5000  #@param\n",
        "\n",
        "time_delta = 0.005\n",
        "\n",
        "expiry = 1.0 \n",
        "\n",
        "number_grid_points = 1024\n",
        "\n",
        "dtype = tf.float64\n",
        "\n",
        "# Generate volatilities, rates, strikes\n",
        "volatility, risk_free_rate, strike = option_param(number_of_options, dtype)\n",
        "\n",
        "device = \"/gpu:0\"\n",
        "with tf.device(device):\n",
        "  \n",
        "  # Warmup\n",
        "  estimate, _ = american_option(\n",
        "      time_delta=time_delta,\n",
        "      expiry=expiry,\n",
        "      number_grid_points=number_grid_points, \n",
        "      volatility=volatility,\n",
        "      risk_free_rate=risk_free_rate,\n",
        "      strike=strike,\n",
        "      dtype=dtype)\n",
        "\n",
        "  # Timed run\n",
        "  t = time.time()\n",
        "  estimate, _ = american_option(\n",
        "      time_delta=time_delta,\n",
        "      expiry=expiry,\n",
        "      number_grid_points=number_grid_points, \n",
        "      volatility=volatility,\n",
        "      risk_free_rate=risk_free_rate,\n",
        "      strike=strike,\n",
        "      dtype=dtype)\n",
        "  time_gpu = time.time() - t\n",
        "    \n",
        "gpu_options_per_second = number_of_options / time_gpu\n",
        "print('------------------------')\n",
        "print('Tensorflow GPU')\n",
        "print('wall time: ', time_gpu)\n",
        "print('options per second: ', gpu_options_per_second)\n",
        "print('------------------------')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "------------------------\n",
            "Tensorflow GPU\n",
            "wall time:  1.4449708461761475\n",
            "options per second:  3460.2774258259888\n",
            "------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5arAmiJEu_Ip",
        "colab_type": "code",
        "cellView": "form",
        "outputId": "34a411f6-b5aa-472c-dedf-b1679ce832be",
        "colab": {}
      },
      "source": [
        "#@title Tensorflow Finance pricing on CPU\n",
        "\n",
        "number_of_options = 500  #@param\n",
        "\n",
        "time_delta = 0.005\n",
        "\n",
        "expiry = 1.0 \n",
        "\n",
        "number_grid_points = 1024\n",
        "\n",
        "dtype = tf.float64\n",
        "\n",
        "# Generate volatilities, rates, strikes\n",
        "volatility, risk_free_rate, strike = option_param(number_of_options, dtype)\n",
        "\n",
        "device = \"/cpu:0\"\n",
        "with tf.device(device):\n",
        "  \n",
        "  # Warmup\n",
        "  estimate, _ = american_option(\n",
        "      time_delta=time_delta,\n",
        "      expiry=expiry,\n",
        "      number_grid_points=number_grid_points, \n",
        "      volatility=volatility,\n",
        "      risk_free_rate=risk_free_rate,\n",
        "      strike=strike,\n",
        "      dtype=dtype)\n",
        "\n",
        "  # Timed run\n",
        "  t = time.time()\n",
        "  estimate, _ = american_option(\n",
        "      time_delta=time_delta,\n",
        "      expiry=expiry,\n",
        "      number_grid_points=number_grid_points, \n",
        "      volatility=volatility,\n",
        "      risk_free_rate=risk_free_rate,\n",
        "      strike=strike,\n",
        "      dtype=dtype)\n",
        "  time_cpu = time.time() - t\n",
        "\n",
        "cpu_options_per_second = number_of_options / time_cpu\n",
        "print('Tensorflow CPU')\n",
        "print('wall time: ', time_cpu)\n",
        "print('options per second: ', cpu_options_per_second)\n",
        "print('------------------------')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Tensorflow CPU\n",
            "wall time:  3.2718610763549805\n",
            "options per second:  152.818224347418\n",
            "------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "YxjImh_nJzqw",
        "outputId": "3047ab84-e000-4335-9028-745555b8e139",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "#@title Quantlib  pricing\n",
        "\n",
        "# Will run only if QuantLib is installed\n",
        "\n",
        "number_of_options = 5000  #@param\n",
        "\n",
        "time_delta = 0.005\n",
        "\n",
        "expiry = 1.0 \n",
        "\n",
        "number_grid_points = 1024\n",
        "\n",
        "import QuantLib as ql\n",
        "warnings.filterwarnings(\"ignore\",\n",
        "                        category=UserWarning,\n",
        "                        module=\"QuantLib\")\n",
        "calculation_date = ql.Date(1, 1, 2010)\n",
        "maturity_date = ql.Date(1, 1, 2011)\n",
        "day_count = ql.Thirty360()\n",
        "calendar = ql.NullCalendar()\n",
        "\n",
        "ql_strike_price = 50\n",
        "ql_volatility = 0.3\n",
        "ql_risk_free_rate = 0.05\n",
        "option_type = ql.Option.Call\n",
        "\n",
        "ql.Settings.instance().evaluationDate = calculation_date\n",
        "payoff = ql.PlainVanillaPayoff(option_type, ql_strike_price)\n",
        "\n",
        "am_exercise = ql.AmericanExercise(calculation_date, maturity_date)\n",
        "american_option_ql = ql.VanillaOption(payoff, am_exercise)\n",
        "\n",
        "flat_ts = ql.YieldTermStructureHandle(\n",
        "    ql.FlatForward(calculation_date, ql_risk_free_rate, day_count)\n",
        ")\n",
        "\n",
        "flat_vol_ts = ql.BlackVolTermStructureHandle(\n",
        "    ql.BlackConstantVol(calculation_date, calendar, ql_volatility, day_count)\n",
        ")\n",
        "\n",
        "spot_price = 4\n",
        "spot_handle = ql.QuoteHandle(\n",
        "    ql.SimpleQuote(spot_price)\n",
        ")\n",
        "bsm_process = ql.BlackScholesProcess(spot_handle,\n",
        "                                      flat_ts,\n",
        "                                      flat_vol_ts)\n",
        "# Compute the same price number_of_options times for fair time comparison\n",
        "t = time.time()\n",
        "for i in range(number_of_options):  \n",
        "  fd_american_engine = ql.FDAmericanEngine(bsm_process,\n",
        "                                           timeSteps=int(expiry / time_delta),\n",
        "                                           gridPoints=number_grid_points)\n",
        "  american_option_ql.setPricingEngine(fd_american_engine)\n",
        "  price = american_option_ql.NPV()\n",
        "time_ql = time.time() - t\n",
        "\n",
        "ql_options_per_second = number_of_options / time_ql\n",
        "print('------------------------')\n",
        "print('QuantLib')\n",
        "print('wall time: ', time_ql)\n",
        "print('options per second: ', ql_options_per_second)\n",
        "print('------------------------')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "------------------------\n",
            "QuantLib\n",
            "wall time:  39.580143451690674\n",
            "options per second:  126.32596963936531\n",
            "------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "wUZv1UPdJ1DT",
        "outputId": "a298ea0f-9ba0-4c7a-d0bf-89f1df64ed3f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 429
        }
      },
      "source": [
        "#@title Tensorflow Finance vs QuantLib\n",
        "# Throughput\n",
        "times_pd = pd.DataFrame([('QuantLib', ql_options_per_second), \n",
        "                         ('CPU', cpu_options_per_second), \n",
        "                         ('GPU', gpu_options_per_second)],\n",
        "                         columns=['Device', 'Options/sec'])\n",
        "sns.set(style=\"darkgrid\", palette=\"Paired\")\n",
        "sns.set_context(\"notebook\", font_scale=1.25, rc={\"lines.linewidth\": 2.5})\n",
        "plt.figure(figsize=(12, 6))\n",
        "pt = sns.barplot(y=\"Device\", x=\"Options/sec\", data=times_pd)\n",
        "pt.axes.set_title(\"Device Option Pricing Speed\", fontsize=25)\n",
        "xlabel = pt.axes.get_xlabel()\n",
        "ylabel = pt.axes.get_ylabel()\n",
        "pt.axes.set_xlabel(xlabel, fontsize=20)\n",
        "pt.axes.set_ylabel(ylabel, fontsize=20)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "lr3FSrVfSpk6",
        "outputId": "968bd7e7-2f19-4844-8743-02dddfb9eebf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        }
      },
      "source": [
        "#@title Time to price a batch of options (GPU vs QuantLib)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import time\n",
        "batch_of_options = [1, 10, 100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000]  #@param\n",
        "\n",
        "gpu_times = []\n",
        "cpu_times = []\n",
        "\n",
        "\n",
        "for options in batch_of_options:\n",
        "    \n",
        "  # Generate volatilities, rates, strikes\n",
        "  volatility, risk_free_rate, strike = option_param(options, dtype)\n",
        "\n",
        "  with tf.device(\"/gpu:0\"):\n",
        "    \n",
        "    # Warmup\n",
        "    estimate, _ = american_option(\n",
        "        time_delta=time_delta,\n",
        "        expiry=expiry,\n",
        "        number_grid_points=number_grid_points,\n",
        "        volatility=volatility,\n",
        "        risk_free_rate=risk_free_rate,\n",
        "        strike=strike,\n",
        "        dtype=dtype)\n",
        "    \n",
        "    # Timed run\n",
        "    t = time.time()\n",
        "    estimate, _ = american_option(\n",
        "        time_delta=time_delta,\n",
        "        expiry=expiry,\n",
        "        number_grid_points=number_grid_points,\n",
        "        volatility=volatility,\n",
        "        risk_free_rate=risk_free_rate,\n",
        "        strike=strike,\n",
        "        dtype=dtype)\n",
        "    time_gpu = time.time() - t\n",
        "    \n",
        "  gpu_times.append(time_gpu)\n",
        "\n",
        "# We hardcode QunatLib values here for simplicity\n",
        "ql_times = [29.9 / 5000 * i for i in batch_of_options]\n",
        "\n",
        "# Prepare Plotting \n",
        "plt.figure(figsize=(12, 6))\n",
        "sns.set(style=\"darkgrid\")\n",
        "sns.set_context(\"paper\", font_scale=1.5, rc={\"lines.linewidth\": 2.5})\n",
        "batches = batch_of_options * 2\n",
        "num_batches = len(batch_of_options)\n",
        "method = [\"Quantlib\"] * num_batches +  [\"Tensorflow\"] * num_batches\n",
        "times = ql_times + gpu_times\n",
        "data = {\"Batch Size\": batches,\n",
        "        \"Method\": method,\n",
        "        \"Times\": times}\n",
        "ql_gpu_times = pd.DataFrame(data = data)\n",
        "plot = sns.lineplot(x=\"Batch Size\", y=\"Times\", hue=\"Method\", style = \"Method\",\n",
        "                    data=ql_gpu_times, markers=True, dashes=False, color=('darkorange',\n",
        "                                                                          'royalblue'))\n",
        "handles, labels = plot.get_legend_handles_labels()\n",
        "plot.legend(handles=handles[1:], labels=labels[1:], loc=\"upper left\")\n",
        "plot.axes.set_title(\"Option Compute Time by Batch Size\",fontsize=25)\n",
        "xlabel = plot.axes.get_xlabel()\n",
        "plot.axes.set_xlabel(xlabel, fontsize=20)\n",
        "plot.axes.set_ylabel('Time in seconds', fontsize=20)\n",
        "plt.setp(plot.get_legend().get_title(), fontsize=28)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "yC193tVOx_cc",
        "outputId": "929e4bba-0928-41ff-8133-257d7389ebbf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 429
        }
      },
      "source": [
        "#@title Options per second depending on the batch size\n",
        "\n",
        "batch_of_options = [1, 10, 100, 1000, 2000, 4000, 5000]  #@param\n",
        "gpu_times = []\n",
        "cpu_times = []\n",
        "\n",
        "for options in batch_of_options:\n",
        "    \n",
        "  with tf.device(\"/gpu:0\"):\n",
        "        \n",
        "    # Generate volatilities, rates, strikes\n",
        "    volatility, risk_free_rate, strike = option_param(options, dtype)\n",
        "    \n",
        "    # Warmup\n",
        "    estimate = american_option(\n",
        "        time_delta=time_delta,\n",
        "        expiry=expiry,\n",
        "        number_grid_points=number_grid_points,\n",
        "        volatility=volatility,\n",
        "        risk_free_rate=risk_free_rate,\n",
        "        strike=strike,\n",
        "        dtype=dtype)\n",
        "    \n",
        "    # Timed run\n",
        "    t = time.time()\n",
        "    estimate = american_option(\n",
        "        time_delta=time_delta,\n",
        "        expiry=expiry,\n",
        "        number_grid_points=number_grid_points,\n",
        "        volatility=volatility,\n",
        "        risk_free_rate=risk_free_rate,\n",
        "        strike=strike,\n",
        "        dtype=dtype)\n",
        "    time_gpu = time.time() - t\n",
        "\n",
        "  gpu_times.append(options / time_gpu)\n",
        "\n",
        "for options in batch_of_options:\n",
        "\n",
        "  with tf.device(\"/cpu:0\"):\n",
        "        \n",
        "    # Generate volatilities, rates, strikes\n",
        "    volatility, risk_free_rate, strike = option_param(options, dtype)\n",
        "    \n",
        "    # Warmup\n",
        "    estimate = american_option(\n",
        "        time_delta=time_delta,\n",
        "        expiry=expiry,\n",
        "        number_grid_points=number_grid_points,\n",
        "        volatility=volatility,\n",
        "        risk_free_rate=risk_free_rate,\n",
        "        strike=strike,\n",
        "        dtype=dtype)\n",
        "    \n",
        "    # Timed run\n",
        "    t = time.time()\n",
        "    estimate = american_option(\n",
        "        time_delta=time_delta,\n",
        "        expiry=expiry,\n",
        "        number_grid_points=number_grid_points,\n",
        "        volatility=volatility,\n",
        "        risk_free_rate=risk_free_rate,\n",
        "        strike=strike,\n",
        "        dtype=dtype)\n",
        "    time_cpu = time.time() - t\n",
        "    \n",
        "  cpu_times.append(options / time_cpu)\n",
        "\n",
        "# Prepare data for plotting\n",
        "plt.figure(figsize=(12, 6))\n",
        "batches = batch_of_options * 2\n",
        "num_batches = len(batch_of_options)\n",
        "method = [\"GPU\"] * num_batches +  [\"CPU\"] * num_batches\n",
        "times = gpu_times + cpu_times\n",
        "data = {\"Batch Size\": batches,\n",
        "        \"Hardware\": method,\n",
        "        \"Options/Sec\": times}\n",
        "gpu_cpu_times = pd.DataFrame(data = data)\n",
        "sns.set(style=\"darkgrid\", palette=\"Paired\")\n",
        "sns.set_context(\"notebook\", font_scale=1.25, rc={\"lines.linewidth\": 2.5})\n",
        "pt = sns.barplot(x=\"Batch Size\", y=\"Options/Sec\",hue=\"Hardware\", data=gpu_cpu_times)\n",
        "pt.axes.set_title(\"Batched Options Priced per Second (GPU vs CPU)\",fontsize=25)\n",
        "xlabel = pt.axes.get_xlabel()\n",
        "ylabel = pt.axes.get_ylabel()\n",
        "pt.axes.set_xlabel(xlabel, fontsize=20)\n",
        "pt.axes.set_ylabel(ylabel, fontsize=20)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "x9b6crfFpYf6",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}